2 Two brands of car battery, ‘Invincible’ and ‘Excelsior’, have lifetimes which are normally distributed. Invincible batteries have a mean lifetime of 5 years with standard deviation 0.7 years. Excelsior batteries have a mean lifetime of 4.5 years with standard deviation 0.5 years. Random samples of 20 Invincible batteries and 25 Excelsior batteries are selected and the sample mean lifetimes are \(\bar { X } _ { I }\) years and \(\bar { X } _ { E }\) years respectively.

1. State the distributions of \(\bar { X } _ { I }\) and \(\bar { X } _ { E }\).
2. Calculate \(\mathrm { P } \left( \bar { X } _ { I } - \bar { X } _ { E } \geqslant 1 \right)\).